document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=867851>Question 867851</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A certain radioactive substance decays according to the formula q(t)= q0e^-.0063t. where q0 is the initial amount of the substance and t is the time in days. Approximate the half-life of the substance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #523230 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=523230\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A certain radioactive substance decays according to the formula q(t)= q0e^-.0063t. where q0 is the initial amount of the substance and t is the time in days. Approximate the half-life of the substance.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let Qo = 1, then Q(t) = .5<BR>\n" );
document.write( "A simple equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ae%5E%28-.0063t%29+=+.5 ALIGN=MIDDLE  ALT=\"1%2Ae%5E%28-.0063t%29+=+.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "find the ln of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%5E%28-.0063t%29%29+=+ln%28.5%29 ALIGN=MIDDLE  ALT=\"ln%28e%5E%28-.0063t%29%29+=+ln%28.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the log equiv of exponents<BR>\n" );
document.write( "-.0063t*ln(e) = ln(.5)<BR>\n" );
document.write( "the ln of e is one so we have<BR>\n" );
document.write( "-.0063t = -.693147<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-.693147%29%2F%28-.0063%29 ALIGN=MIDDLE  ALT=\"%28-.693147%29%2F%28-.0063%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = +110 days is the half life of the substance </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );